Matrices with convolutions of binomial functions and Krawtchouk matrices |
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Authors: | Norman C. Severo |
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Affiliation: | aState University of New York at Buffalo, USA |
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Abstract: | We introduce a class SN of matrices whose elements are terms of convolutions of binomial functions of complex numbers. A multiplication theorem is proved for elements of SN. The multiplication theorem establishes a homomorphism of the group of 2 by 2 nonsingular matrices with complex elements into a group GN contained in SN. As a direct consequence of representation theory, we also present related spectral representations for special members of GN. We show that a subset of GN constitutes the system of Krawtchouk matrices, which extends published results for the symmetric case. |
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Keywords: | Matrices Convolution of binomial functions Multiplication theorem Representation theory Krawtchouk matrices |
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